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4-- 


SPIRALS 

for 

Street     Railway     Curves     and 
Easement    Curves 

for 

treet  Railway  Branch-Off  s 


OF  THE 

UNIVERSITY 


Complete  Formulas  and  Tables 


The  Pennsylvania  Steel  Company 

a    I  . 

Steelton,  Pa. 
FROG    AND    SWITCH    DEPARTMENT 

Copyright  1906  by  The  Pennsylvania  Steel  Company,  SteeUon,  Pa. 


THE    PENNSYLVANIA    STEEL    COMPANY 


LIST  OF  OFFICES 


1  ne  Pennsylvania  kteel  (Company 

GENERAL  SALES  OFFICE 
Philadelphia,  Pa.,  Girard  Trust  Building 

Cable  .A/Jress,  Penns/ee/,  Philadelphia.  (l/se  Lieber's  Code.) 

BALTIMORE,  MD.       .     .  Continental  Trust  Building 

BOSTON,  MASS.      .     .     .  .     .     .     .       70  Kilby  Street 

CHICAGO,  ILL.      .  '   .     .  .     Western  Union  Building 
LONDON,  ENG  .....     110  Cannon  Street,  E.  C. 

MEXICO,  MEX.      ...  76  Calle  de  Cinco  de  Mayo 

NEW  YORK  CITY,  N.  Y.  ...     .     .     71  Broadway 

PHILADELPHIA,  PA.    .     .  .       Girard  Trust  Building 

SAN  FRANCISCO,  CAL.     .  -£ 


ST.  Louis,  Mo.      .      Commonwealth  Trust  Building 
STEELTON,  PA  ...........      Works 


THE    PENNSYLVANIA    STEEL    COMPANY  5 

JHE  Spiral  System  presented 
in  the  following  pages  has 
been  in  use  by  The  Penn- 
sylvania Steel  Company  for  the  last 
decade,  and  has  given  general  satis- 
faction. It  consists  of  a  transition 
formed  of  arcs  of  diminishing  radii, 
and  is  calculated  upon  the  center  line 
of  track,  since  that  is  substantially  the 
path  followed  by  the  center  of  gravity 
of  the  cars.  The  purpose  of  a  spiral 
ending  on  a  short  radius  street  railway 
curve  is  not  as  in  steam  railroad  prac- 
tice, to  enable  the  super-elevation  of 
the  outer  rail  of  curve  to  be  gradually 
attained,  but  to  reduce  the  shock  due 
to  the  change  in  direction  of  the  car. 
The  switch  easements  are  so  designed 
that  a  plain  curve  can  be  converted 


1 


6  THE    PENNSYLVANIA    STEEL    COMPANY 

into  a  branch-off  with  the  minimum 
disturbance  of  existing  work  while  re- 
taining standard  switches  and  mates, 
and  some  simplification  of  computation 
is  also  obtained.  The  solutions  of  the 
various  problems  given  present  suffi- 
cient information  to  enable  any  data 
required  for  the  laying  out  or  con- 
struction of  track  to  be  readily  secured. 


THE    PENNSYLVANIA    STEEL    COMPANY 


PROBLEM  1.     To  select  a  spiral. 

(a)  The  radius  of  the  main  curve  must  be  less 
than  the  preceding  branch  of  the  spiral,  must  be 
more  than  the  next  branch  would  be  were  it  pro- 
duced, and  should  nearly  equal  the  latter. 

(b]  The  longer  the  spiral,  the  easier  the  entrance 
will  be.     But  bear  in  mind  that  the  main  body  of  the 
curve  should  be  circular,  the  spiral  simply  acting  as 
an  entrance  to  it. 

(c}  A  spiral  of  less  than  three  branches  should 
not  be  used. 


Problem 


PROBLEM  2.     Given:     A  circular  curve  with  sym- 
metrical  spirals,  to  find  the  tangent  and  external 

distances. 

O  G— R+X— versine  S°  R; 
GS=Y— sineS°R; 


THE    PENNSYLVANIA    STEEL    COMPANY 


Tangent  distance— O  G  tan  y2  A  +G  S ; 
External  distance— O  G  ex  sec  V2  A  +X- 
S°  R. 


PROBLEM  3.     Given :     The  tangent  distance  V  S, 
the  intersection  angle  A,  and  the  desired  length  of 
spiral,  to  find  the  radius  of  the  curve.     Approximate 
R=cotangent  yz  A(V  S  — ^  length  of  spiral).     Hav- 
ing selected  a  spiral  by  this  radius,  the  exact  radius 
may  be  found,  if  required,  by  the  following  formula : 
p  _cos  y2  A  (V  S— Y— X  tan  y2  A  ) 
sine  (y2  A — S) 

Caution — If  the  result  is  enough  different  from 
the  original  radius  to  require  a  change  in  the  spiral 
by  Problem  1,  a  second  trial  must  be  made. 

PROBLEM  4.     Given :     The   intersection   angle  A 


THE    PENNSYLVANIA    STEEL    COMPANY 


and  the  external  distance  V  H,  to  find  the  radius. 
Approximate  to  the  radius  by  finding  that  for  a 
simple  curve  passing  through  the  point  H,  and  select 
a  spiral  for  a  radius  somewhat  smaller. 
Then  R=VHcosKA-X 
cos  S  —  cos  y2  A 

Caution — If  the  result  is  enough  different  from 
the  original  radius  to  require  a  change  in  the  spiral 
by  Problem  1,  a  second  trial  must  be  made. 


Problems  5  and  6 

PROBLEM  5.  Given :  The  X  and  Y  for  any  point 
on  the  spiral ;  to  find  the  deflection  from  the  tangent 
at  the  point  of  spiral. 

Tangent  deflection  angle^^- 

PROBLEM  6.  Given :  The  X  and  Y  for  any  point 
on  the  spiral,  to  find  the  long  chord. 

Y 

(a)  Long  chords : -j— -. — . 

cosine  det  angle 

or  (b]  Long  chord  ^^/xa-i-Y2. 
PROBLEM  7.     Given :     X  and  Y  for  a  point  on  the 
spiral, -to  find  X'  and  Y'  on  a  line  parallel  to  the 
spiral,  and  offset  the  distance  S  S'  inside  the  spiral. 
X'=X— S  S'  versine  S°; 
Y'=Y— SS'sineS0. 

Note — Problems  5  and  6  can  then  be  applied  to  X' 
and  Y'  if  it  is  desired  to  use  deflection  angles  to  lay 
out  the  curve. 


10         THE    PENNSYLVANIA    STEEL    COMPANY 


— it. 


Problem  7 


As  these  curves  will  almost  invariably  be  laid  out 
on  an  offset  varying  with  the  gage  of  the  road,  the 
deflections  are  not  figured  in  the  table. 


Problem  8 

PROBLEMS.  Given: 
A  circular  curve  with  spi- 
rals to  find   the   distance 
V  V,  in  order  to  lay  out  a 


THE    PENNSYLVANIA    STEEL    COMPANY         11 


tangent  to  the  circular  curve,  from  which  the  latter 
may  be  laid  out  in  the  usual  manner. 

V  H  =  see  Problem  2; 

V  H=R  ex  secant  (^  A  —  S) ; 

V  V'=VH— V  H. 


-Jt-L 


------s-- 


PROBLEM  9.     General  solution  for  unsymmetrical 
curves. 

O  G=R+X— R  versine  S° ; 
-G  S=Y— R  sine  S°; 
O  G'— R+X'— R  versine  S°' ; 
GS'=Y— RsineS0'; 

V  S=tan  y2  AO  G+G  S°  G'~ 


V  S'=tan  yz  AO  G+G'  S'± 


sine  A 
Q  G'— O  G 

tan  A 


12 


THE    PENNSYLVANIA    STEEL    COMPANY 


Note — ±  in  above;    +  if   A   is  more  than  90°, 
and  —  if  A  is  less  than  90°. 

A'=  A  —  (S°+S0/); 
V  Lor  V  L'=tan  #A'  R; 

V  B=X+V  LsineS0; 
VB=VS  —  (Y+V  L— VLversine  S°); 


VV'  =     VB      ifC=450-; 
cosine  C 

VV'=-X^if  C=45°+. 
sine  C 


PROBLEM  10.  Given :  The  middle  ordinate  for  a 
chord  of  length  a  b  for  R  and  R',  to  find  the  middle 
ordinate  at  the  P  C  C.  From  the  figure  it  is  evident 
that  d'  c'  bisects  c  d. 


.-.  ef= 


cf+df 
2 


Therefore,  the  middle  ordinate  at  any  P  C  C  in  the 
spiral  equals  one-half  the  sum  of  the  middle*  ordi- 
nates  for  the  radii  on  each  side  for  the  same  chord. 


THE    PENNSYLVANIA    STEEL    COMPANY         13 


•  D' 


v. 


A  F  B 

Problem  11 

PROBLEM  11.  Given:  That  portion  of  a  spiral 
with  equal  chords  L,  L'  and  L"  and  angles  a — b,  a, 
and  a+b,  to  find  the  middle  ordinate  at  the  center  of 
the  chord  L  in  the  length  D'  C'. 

CF=C'  AandDF=D'B. 

From  the  figure  it  is  evident  that  D'  C'  bisects  C  D. 
CF+DF 


.-.  E  F=- 


2 


Then  C'  A=%  L  tan  tfa+L'  sine  (%  a 
D'  B— y2  L  tan  X«+L"  sine  (K  a 

and  since  the  sines  of  small  angles  are  proportional 
to  the  angles, 

C  F+D  F 

=E  F=X  L  tan  %  a+L,  sine  a. 

But  this  last  equation  equals  the  middle  ordinate  in 
the  length  A  B  for  the  radius  of  the  central  arc ;  and 
since  the  increment  to  the  angle  b  would  be  equal  if 
L'  and  L"  were  equal,  the  middle  ordinate  at  the 
center  of  any  arc  of  the  spiral,  for  any  length  of 
chord,  is  equal  to  the  middle  ordinate  of  the  radius 
of  that  arc  in  the  same  length. 


THE    PENNSYLVANIA    STEEL    COMPANY         15 


Standard  Spirals. 
The  Pennsylvania  Steel  Co 


Center   Line   Data. 


16         THE    PENNSYLVANIA    STEEL    COMPANY 

SPIRAL   No.  2 

Rad. 

Angle 

X 

Y 

O 

Versine 

Sine 

300 
150 
100 

75 
60 
50 
42^ 
37^ 

0°-30' 
1°-00' 
1°-30' 
2°-00' 
2°-30' 
3°-00' 
3°-30' 
4°-00' 

0.011 
0.057 
0.160 
0.342 
0.627 
1.036 
1.587 
2.309 

2.618 
5.235 
7.851 
10.463 
13.065 
15.651 
18.187 
20.703 

0°-30' 
1°-30' 
3°-00' 
5°-00' 
7°-30' 
10°-30' 
14°-00' 
18°-00' 

.00004 
.00034 
.00137 
.00381 
.00856 
.01675 
.02970 
.04894 

.00873 
.02618 
05234 
.08716 
.  13053 
.18224 
.24192 
.30902 

SWITCH    EASEMENT   S  2-75 

Rad. 

Angle 

X 

Y 

s° 

This    Ease- 
ment gives  an 
O  G  equal  to 
and    a    G    S 
3.  346  less  than 
vSpiral  No.  2. 

75 

45K 
42^ 
37^ 

7°-50' 

2°-40' 
3°-30' 
4°-00' 

0.700 
1.036 
1.587 
2.309 

10.222 
12.305 
14.841 
17.357 

7°-50' 
10°-30' 
14°-00' 
18°-00' 

SPIRAL   No.  2^ 

Rad. 

Angle 

x 

Y 

s° 

Versine 

Sine 

444 
222 

148 
111 
89 

74 
63^ 
55^ 
49 
44X 
40^ 

0°-20' 
0°-40' 
1°-00' 
1°-20' 
1°-40' 
2°-00' 
2°-20' 
2°-40' 
3°-00' 
3°-20' 
3°-40' 

0.007 
0.038 
0.105 
0.226 
0.414 
0.684 
1.051 
1.529 
2.128 
2.870 
3.763 

2.583 
5.166 

7.748 
10.328 
12.910 
15.478 
18.038 
20.576 
23.070 
25.550 
27.983 

0°-20' 
1°-00' 
2°-00' 
3°-20' 
5°-00' 
7°-00' 
9°-20' 
12°-00' 
15°-00' 
18°-20' 
22°-00' 

.00002 
00015 
.00061 
.00169 
00381 
.00745 
.01324 
.02185 
.03407 
.05076 
.07282 

.00582 
.01745 
.03490 
.05814 
.08716, 
.12187 
.16218 
.20791 
.25882 
.31454 
.37461 

THE    PENNSYLVANIA    STEEL    COMPANY         17 

SWITCH    EASEMENT    S  2^-100 

Rad. 

Angle 

X 

Y 

o 

This 

Ease- 

ment  gives  an 

102^ 

6°-30' 

0.658 

11.584 

6°-30' 

O  G  equal  to 

56X 

5°-30' 

1.529 

16.936 

12°-00' 

and    a 

G    S 

49 

44^ 
40^ 

3°-00' 
3°-20' 
3°-40' 

2.128 
2.870 
3.763 

19.430 
21.910 
24.343 

15°-00' 
18°-20' 
22°-00' 

3.  640  less  than 
Spiral  No.  2|-. 

SWITCH    EASEMENT   S  2^-200 

Rad. 

Angle 

X 

Y 

s° 

Tvjiic 

200 

4°-00' 

0.487 

13.951 

4°-00' 

ment  gives  an 

129 

1°-00' 

0.664 

16.196 

5°-00' 

O    G 

0.250 

74 
63^ 
55^ 
49 

2°-00' 
2°-20' 
2°-40' 
3°-00' 

0.934 
1.301 
1.779 

2.378 

18.764 
21.324 
23.862 
26.356 

7°-00' 
9°-20' 
12°-00' 
15°-00' 

greater 
G     S 
greater 

and  a 
3.286 

than 

44^ 

3°-20' 

3.120 

28.836 

18°-20' 

Spiral  No.  2£. 

40^ 

3°-40' 

4.013 

31.269 

22°-00' 

SPIRAL   No.  3 

Rad. 

Angle 

X 

Y 

s° 

Versine 

Sine 

300 

1°-00' 

0.046 

5.236 

1°-00' 

.00015 

.01745 

150 

2°-00' 

0.229 

10.468 

3°-00' 

.00137 

.05234 

100 

3°-00' 

0.639 

15.688 

6°-00' 

.00548 

.10453 

75 

4°-00' 

1.368 

20.871 

10°-00' 

.01519 

.17365 

60 

5°-00' 

2.501 

25.982 

15°-00' 

.03407 

.25882 

50 

6°-00' 

4.118 

30.959 

21°-00' 

.06642 

.35837 

40 

7°-00' 

6.143 

35.403 

28°-00' 

.11705 

.46947 

18         THE    PENNSYLVANIA    STEEL    COMPANY 

SWITCH   EASEMENT   S  3-100 

Rad. 

Angle 

X 

Y 

S° 

This    Ease- 
ment gives  an 
O  G  equal  to 
and    a     G    S 
4.  391  less  than 
Spiral  No.  3. 

102X 
81 
60 
50 

40 

6°-30' 
3°-30' 
5°-00' 
6°-00' 
7°-00' 

0.658 
1.368 
2.501 
4.118 
6.143 

11.584 
16.480 
21.591 
26.568 
31.012 

6°-30 
10°-00' 
15°-00' 
21°-00' 
28°-00' 

SWITCH   EASEMENT   S  3-200 

Rad. 

Angle 

X 

Y 

S° 

This    Ease- 
ment gives  an 
O    G    0.250 
greater  and  a 
G     S    2.853 
greater    than 
Spiral  No.  3. 

200 
132 
75 
60 
50 
40 

4°-00' 
2°-00' 
4°-00' 
5°-00' 
6°-00' 
7°-00' 

0.487 
0.889 
1.618 
2.751 
4.368 
6.393 

13.951 
18.541 
23.724 
28.835 
33.812 
38.256 

4°-00' 
6°-00' 
10°-00' 
15°-00' 
21°-00' 
28°-00' 

SPIRAL  No.  4 

Rad. 

Angle 

X 

Y 

Co 

Versine 

Sine 

420 
210 
140 
105 
84 
70 
60 

0°-42' 
l°-24' 
2°-06' 
2°-48' 
3°-30' 
4°-12' 
4°-54' 

0.031 
0.157 
0.439 
0.939 
1.720 
2.839 
4.352 

5.131 
10.261 
15.384 
20.490 
25.561 
30.567 
35.469 

0°-42' 
2°-06' 
4°-12' 
7°-00' 
10°-30' 
14°-42' 
19°-36' 

.00007 
.00067 
.00269 
.00745 
.01675 
.03273 
.05794 

.01222 
.03664 
.07324 
.12187 
.  18224 
.25376 
.33545 

SWITCH    EASEMENT   S  4-200 

Rad. 

Angle 

X 

Y 

s° 

This    Ease- 
ment gives  an 
O    G    0.178 
greater  and  a 
G  S  equal   to 
Spiral  No.  4. 

200 
125^ 
84 
70 
60 

4°-00' 
3°-00' 
3°-30' 
4°-12' 
4°-54' 

0.487 
1.117 
1.898 
3.017 
4.530 

13.951 
20.490 
25.561 
30.567 
35.469 

4°-00' 
7°-00' 
10°-30' 
14°-42' 
19°-36' 

THE    PENNSYLVANIA    STEEL    COMPANY         19 

SPIRAL   No.    5 

Rad. 

Angle 

X 

Y 

S° 

Versine 

Sine 

600 
300 
200 
150 
120 
100 
85 

0°-30' 
1°-00' 
1°-30' 
2°-00' 
2°-30' 
3°-00' 
3°-30' 

0.023 
0.114 
0.320 
0.685 
1.255 
2.073 
3.175 

5.236 
10.471 
15.703 
20.926 
26.130 
31.302 
36.374 

0°-30' 
1°-30' 
3°-00' 
5°-00' 
7°-30' 
10°-30' 
14°-00' 

.00004 
.00034 
.00137 
.00381 
.00856 
.01675 
.02970 

.00873 
.02618 
.05234 
.08716 
.13053 
.18224 
.24192 

SWITCH    EASEMENT   S  5-200 

Rad. 

Angle 

X 

Y 

S° 

This    Ease- 
ment gives  an 
O  G  equal  to 
and     a     G    S 

4.  468  less  than 
Spiral  No.  5. 

200 
144 
120 
100 

85 

4°-00' 
1°-00' 
2°-30' 
3°-00' 
3°-30' 

0.487 
0.685 
1.255 
2.073 
3.175 

13.951 
16.458 
21.662 
26.834 
31.906 

4°-00' 
5°-00' 
7°-30' 
10°-30' 
14°-00' 

SPIRAL   No.  6 

Rad. 

Angle 

X 

Y 

S° 

Versine 

Sine 

900 
450 
300 
225 
180 
150 
128 

0°-20' 
0°-40' 
1°-00' 
1°-20' 
l°-4Q' 
2°-00' 
2°-20' 

0.015 
0.076 
0.213 
0.457 
0.837 
1.385 
2.125 

5.236 
10.472 
15.706 
20.936 
26.158 
31.365 
36.524 

0°-20' 
1°-00' 
2°-00' 
3°-20' 
5°-00' 
7°-00' 
9°-20' 

.00002 
.00015 
.00061 
.00169 
.00381 
.00745 
.01324 

.00582 
.01745 
.03490 
.05814 
.08716 
.12187 
.16218 

SWITCH    EASEMENT    S  6-200 

Rad. 

Angle 

X 

Y 

S° 

This    Ease- 
ment gives  an 
O  G  equal  to 
and     a    G    S 
7.  770  less  than 
Spiral  No.  6. 

200 
255 
150 

128 

4°-00' 
1°-00' 
2°-00' 

2°-20' 

0.487 
0.837 
1.385 
2.125 

13.951 
18.388 
23.595 

28.754 

4°-00' 
5°-00' 
7°-00' 
9°-20' 

20         THE    PENNSYLVANIA    STEEL    COMPANY 

SPIRAL   No.  7 

Rad. 

Angle 

X 

Y 

S° 

Versine 

Sine 

1260 

0°-15' 

0.012 

5.498 

0°-15' 

.00001 

.00436 

630 

0°-30' 

0.060 

10.995 

0°-45' 

.00009 

.01309 

420 

0°-45' 

0.168 

16.492 

1°-30' 

.00034 

.02618 

315 

1°-00' 

0.360 

21.987 

2°-30' 

.00095 

.04362 

252 

1°-15' 

0.660 

27.475 

3°-45' 

.00214 

.06540 

210 

1°-30' 

1.091 

32.957 

5°-15' 

.00420 

.09150 

180 

l°-45' 

1.678 

38.424 

7°-00' 

.00745 

.12187 

157 

SPIRAL   No.  8 

Rad. 

Angle 

X 

Y 

S° 

Versine 

Sine 

1890 

0°-10' 

0.008 

5.498 

0°-10' 

.00000 

.00291 

945 

0°-20' 

0.040 

10.996 

0°-30' 

.00004 

.00873 

630 

0°-30' 

0.112 

16.493 

1°-00' 

.00015 

.01745 

472^ 

0°^0' 

0.241 

21.990 

1°-40' 

.00042 

.02908 

378 

0°-50' 

0.441 

27.483 

2°-30' 

.00095 

.04362 

315 

1°-00' 

0.729 

32.973 

3°-30' 

.00187 

.06105 

270 

1°-10' 

1.120 

38.457 

4°-40 

.00332 

.08136 

236 

SPIRAL   No.  9 

Rad. 

Angle 

X 

Y 

S° 

Versine 

Sine 

2730 

0°-  7' 

0.006 

5.559 

o°-  r 

.00000 

.00204 

1365 

0°-14' 

0.028 

11.118 

0°-21' 

.00002 

.00611 

910 

0°-21' 

0.079 

16.677 

0°-42' 

.00007 

.01222 

682^ 

0°-28' 

0.170 

22.234 

1°-10 

.00021 

.02036 

546 

0°-35' 

0.311 

27.791 

l°-45' 

.00047 

.03054 

455 

0°-42' 

0.515 

33.346 

2°-27' 

.00091 

.04275 

390 

0°-49' 

0.792 

38.899 

3°-16' 

.00162 

.05698 

341 

THE    PENNSYLVANIA    STEEL    COMPANY         21 

SPIRAL   No.   10 

Rad. 

Angle 

X 

Y 

S° 

Versine 

Sine 

3780 

0°-05' 

0.004 

5.498 

0°-05' 

.00000 

.00145 

1890 

0°-10' 

0.020 

10.996 

0°-15' 

.00001 

.00436 

1260 

0°-15' 

0.056 

16.493 

0°-30' 

.00004 

.00873 

945 

0°-20' 

0.120 

21.991 

0°-50' 

.00011 

.01454 

756 

0°-25' 

0.220 

27.488 

1°-15' 

.00024 

.02181 

630 

0°-30' 

0.364 

32.983 

l°-45' 

.00047 

.03054 

540 

0°-35' 

0.560 

38.478 

2°-20' 

.00083 

.04071 

472 

SPIRAL   No.  11 

Rad. 

Angle 

X 

Y 

o 

Versine 

Sine 

5250 

0°-04' 

.0035 

6.109 

0°-04' 

.00000 

.00116 

2625 

0°-08' 

.0178 

12.217 

0°-12' 

.00001 

.00349 

1750 

0°-12' 

.0498 

18.326 

0°-24' 

.00002 

.00698 

1312^ 

0°-16' 

.1066 

24.434 

0°-40' 

.00007 

.01164 

1050 

0°-20' 

.1955 

30.542 

1°-00' 

.00015 

.01745 

875 

0°-24' 

.3234 

36.649 

l°-24' 

.00030 

.02443 

750 

0°-28' 

.4975 

42.756 

l°-52' 

.00053 

.03257 

656 

SPIRAL   No.  12 

Rad. 

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Y 

s° 

Versine 

Sine 

7140 

0°-03' 

.0027 

6.231 

0°-03' 

.00000 

.00087 

3570 

0°-06' 

.0136 

12.462 

0°-09' 

.00000 

.00262 

2380 

0°-09' 

.0381 

18.692 

0°-18' 

.00001 

.00524 

1785 

0°-12' 

.0816 

24.923 

0°-30' 

.00004 

.00873 

1428 

0°-15' 

.1495 

31.153 

0°-45' 

.00009 

.01309 

1190 

0°-18' 

.2474 

37.384 

1°-03' 

.00017 

.01832 

1020 

0°-21' 

.3806 

43.613 

l°-24' 

.00030 

.02443 

892 

THE    PENNSYLVANIA    STEEL    COMPANY         28 


Tables  giving  elements   of 

SPIRALS 

for      •  \ 

Inner   Gage  Line  Lengths 

of  Rails  and 

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78'-  9X" 

2f-|" 

51'-  8{f  * 

15" 

160'-  OX" 

i**" 

77'-  6" 

2|f" 

51'-  2X" 

»' 

if*" 

76'-  3X" 

3fi" 

50'-  71f 

THE    PENNSYLVANIA    STEEL    COMPANY 


75 


MIDDLE  ORDINATES,  10   FT.  CHORDS 


M.  O. 


Radius 


M.  O. 


Radius 


M.  0. 


Radius 


3" 


£ 


3ff 


50'-  !#' 
49'-  7Ty 
49'-  IX" 
48'-  7^" 
48'-  1TV 

47'-  7^" 
47'-  2Ty 
46-  8}f 
46'-  3^" 
45'-10Ty 

45'-  5TV' 
45'-  0" 
44'-  7" 
44'-  2y8" 
43'-  9^i" 

43'-  4ft' 
43'-  0Ty 

42'-  iy2n 

42'-  3Ty 


41'-  6; 
41'-  ft< 
40-10" 
40'-  5j 
40-  1; 


39'-  6ry 
39-  2A" 


38'-  3}f 
37-11^' 


4" 


4/8 


37'-  8" 
37'-  4; 
37'-  Ij 
36'-  9; 
36'-  6, 


35'- 
35-  5ft" 

OK'         O9" 

OO  —   ^y% 

84'-llA' 

Jt"»: 

34'-  2ft' 
33'-!!^" 


33'-  6X' 

QO'         O  T/  ' 

OO  —    ^5/2 

33'-  Olf ' 
32-10^' 

32-  iy2' 

32'-  4^' 
32'-  2^' 


31'- 
31'- 

31'- 
31'- 
30'-11 
30'-  9 
30'-  7 
30'-  4 


30'-  2}4' 
30'-  OX" 

29'-10TV" 

29-  5lf" 

29'-  3H" 
29'-  1TV" 

28'-  9>^" 
28'-  lyz" 

28-  5>^" 
28'-  %y2" 
28'-  1T9^' 
27'-!!^" 
27-  9X" 

27'-  7^" 
27'-  6" 
27^-  4^ 

27'-  0T9^" 

26'-101f" 
26'-  9Ty 
26'-  7T5ff" 
26'-  5^" 
26'-  31f" 
26'-  2X" 

26^-  0^ 

25;-  7ft; 

25'-  4A' 


76         THE    PENNSYLVANIA    STEEL    COMPANY 

\Vneel   Contours 

GREAT  variety  of  wheel  con- 
tours are  used  on  street  rail- 
ways,  and  often  the  extremes 
are  used  on  the  same  track  sys- 
tem to  the  great  detriment  of  both  special 
work  and  wheels. 

Since  there  are  now  no  standard  wheel 
contours  except  the  M.  C.  B.  (steam  rail- 
road), it  seems  proper  to  offer  some  de- 
signs which  will  meet  most  of  the  difficul- 
ties found  in  our  practice. 

The  contour  of  wheel  fixes  the  charac- 
ter of  the  special  work  as  to  whether  the 
frog  work  is  to  be  "  flange  bearing."  This 
term  means  that  at  the  ''waist  of  frog," 
i.  e.,  just  in  advance  of  the  point  of  frog, 
the  floor  of  the  throat  is  raised  to  carry  the 
wheel  through  the  waist  and  past  the  point 
upon  its  flange.  The  latter  cannot  be  of  a 
shape  or  character  of  metal  well  adapted  to 
this  service,  and  more  or  less  chipped 
flanges  are  thereby  caused.  It  is,  however, 
inevitable  that  this  support  be  provided, 


THE    PENNSYLVANIA    STEEL    COMPANY         77 

unless  the  tread  is  wide  enough  to  carry 
the  wheel  past  this  critical  point. 

Contour  "A"  is  the  M.  C.  B.  standard 
wheel,  and  is  adapted  to  open  track  and 
streets  where  rails  with  deep  and  wide 
flangeways  are  provided,  and  the  paving  is 
such  that  the  tread  will  not  be  seriously 
chipped  by  contact  with  the  same. 

Contour  "B"  is  a  compromise  wheel, 
for  use  where  a  portion  of  the  track  system 
is  used  by  wheels  having  Contour  "A"  and 
the  remainder  has  not  the  deep  flangeway, 
but  the  width  of  flangeway  is  provided.  If 
the  paving  conditions  of  this  .portion  are 
such  that  the  width  of  tread  must  be  re- 
duced from  that  shown,  all  frog  work  on 
the  entire  portion  of  system  used  by  Con- 
tour "B  "  must  be  made  "flange  bearing." 

Contour  "C"  is  adapted  to  track  sys- 
tems where  wide  and  deep  flangeways  can- 
not be  provided  but  the  paving  conditions 
are  such  that  the  width  of  the  tread  shown 
can  be  used. 

Contour  "D"  is  adapted  to  track  sys- 
tems where  a  narrower  tread  is  required  by 


78         THE    PENNSYLVANIA    STEEL    COMPANY 

the  paving  conditions,  the  shape  and  size 
of  flange  being  the  same  as  "  C."  As  wide 
a  tread  as  possible  should  be  used,  as  the 
life  of  special  work  will  thereby  be  mate- 
rially prolonged  besides  increasing  the  fac- 
tor of  safety  on  any  open  track  in  the 
system.  "  Flange-bearing  "  frogs  will  be 
required  for  this  contour. 

Contours  "A"  and  "C"  will  give  the 
best  results  where  conditions  permit  their 
use  and  do  not  require  "flange-bearing" 
frogs. 

Contour  "B"  will  not  give  entire  sat- 
isfaction, since  the  flange  is  not  of  the  best 
shape,  and  should  only  be  used  when  com- 
pelled by  the  conditions  stated. 

Contours  "C"  and  "  D "  can  be  used 
on  the  same  track  system  if  "flange-bear- 
ing "  frogs  are  provided  for  that  portion  on 
which  Contour  "D"  is  used. 

Contours  "C"  and  "D"  cannot  be 
satisfactorily  used  on  track  systems  de- 
signed for  Contours  "A"  or  "B,"  or  vice 
versa. 


THE    PENNSYLVANIA    STEEL    COMPANY         79 


THE    PENNSYLVANIA    STEEL    COMPANY         81 


THE     PENNSYLVANIA    STEEL    COMPANY 


Angles 

Bulb 

Reinforcing 

Switch 

Equal  Legs 

Unequal  Legs 

Braces 

Acme 

Switch 

Guard 

Interlocking 

Tie  Plate 

Bridges 
Buildings 

Chairs 

Rail  chairs  for  steam  railroads  in  paved  streets 

Channels 

Circles 

Turntables 

Coal  storage  tracks 

Clamps 

Guard  rail 

Crossings 

Bolted 

Bolted  Plate 
Keyed 

"  Manard"  Steel 

Movable  Point 
Riveted 

Street  Railway 
"Manard"  Renewable  Centre 
Double  Slip 

Single  Slip 

Three  Rail 


THE    PENNSYLVANIA     STEEL    COMPANY 


DROP  FORGED  SOCKET 


ACME  BRACE 


84         THE    PENNSYLVANIA    STEEL    COMPANY 


MANARD  ANVIL  FACE  FROG,  DESIGN  153 


THE    PENNSYLVANIA     STEEL     COMPANY         85 


MANARD  ANVIL  FACE  SPRING  RAIL  FROG 


THE    PENNSYLVANIA    STEEL    COMPANY 


Crossovers 

Single  Crossovers 

Double  Crossovers 

Portable  Crossovers 
Forgings 

Frogs,    Rigid 

Bolted 

Bolted  Plate 

Keyed 

"Manard"  Steel 

"Manard"  Renewable  Centre 

Riveted 
Frogs,   Spring 
Bolted 

Bolted  Plate 

Double 

Hinged 

Keyed 
"Manard"  Steel 

Riveted  Plate 
Twin 

Vaughan  Hinged 

Vaughan  Sliding 
Joints 

Angle 

Channel 

Compromise 

Deep  Girder  Rail 

Plain 
Knees 

Mates  ' 

Built 

"Manard"  Bolted 

"Manard"  Key  Fast 
Plates 

.  Frog 

Slide 

Switch 

Tie 
Rails,  Guard 


THE    PENNSYLVANIA    STEEL    COMPANY 


MANARD  GROOVED  TONGUE  SWITCH  FOR  STEAM 
RAILROADS  IN  PAVED  STREETS 


88 


THE     PENNSYLVANIA    STEEL    COMPANY 


THE    PENNSYLVANIA    STEEL    COMPANY         89 


RAPID  RENEWABLE  MANARD  CENTRE  FROG 


90         THE    PENNSYLVANIA    STEEL    COMPANY 


Rails 

A.  S.  C.  E.  Sections 

Cast  Weld  Compromise 
Check 

Flat 

Girder 
Girder  Guard 

Slot  Rails  and  Conductor  Bars 
Tee 

High  Tee 

Tram 
Rails,  Renewable  Guard 

Rods,  Switch  Connecting 

Splice  Bars 

Spikes 

Spiral  Curves 

Steam  Railroad  Track  Equipment 

Street    Railway  Special  Work 

Street  Railway  Track  Fastenings 

Steel 

Bessemer 
Billets 

Blooms 

Castings 

Forgings 

Flats 

Basic  Open  Hearth  Acid  Open  Hearth 

"  Manard  " 

Merchant 

Round 

Shapes 

Slabs 

Special 

Square 

Tool 
Structural  Steel 


THE    PENNSYLVANIA    STEEL    COMPANY 


91 


92         THE    PENNSYLVANIA    STEEL    COMPANY 


GROUND  LEVER,  MODEL  16 


Low  NEW  CENTURY  ADJUSTABLE  SWITCH  STAND 
MODEL  51 A 


THE    PENNSYLVANIA    STEEL    COMPANY 


INTERMEDIATE  MAIN  LINE  SWITCH  STAND 
MODEL  47  B 


94         THE     PENNSYLVANIA    STEEL    COMPANY 


Switches 

Adjustable 
Angle 

Challenge 

Lorenz 

"  Manard  "  Big  Pin  Grooved  Tongue 

"  Manard  "  Big  Pin  Tongue 
"Manard"  Steel 

Plain 

Reinforced 
Socket 

Stub 

Three  Way 
Switch  Stands 
Automatic 
Banner 

Steelton  Detective 
Ground  Levers 

Upright  Levers 

Long  Safety 
Main  Line  Adjustable 
Positive 
Automatic 
Mine 

Mine  Kickover 
New  Century 

New  Century  Adjustable 
New  Era 

Pet 
Semaphore  with  disappearing  blade 

Spring  Ground  Throw 

Tie  Plates  Yard  Stands 

Tie  Rods 
Track  Bolts 
Track  Fastenings 
Track  Girders 

Track  Material  of  All  Kinds 
Trough  Floors 
Trough  Sections 
Viaducts 
"Z"  Bars 


THE    PENNSYLVANIA    STEEL    COMPANY         95 


INTERMEDIATE  SEMAPHORE  SWITCH  STAND,  MODEL  50  E 


THE     PENNSYLVANIA    STEEL    COMPANY 


OF  THE 

UNIVERSITY 

OF 


Chasmar-Winchell  Press     New  York  and  Pittsburgh 


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